Fermat’s Last Theorem Essay -- Pierre Fermat Math Mathematics Papers

Fermat’s Last Theorem The year is 1637. Pierre de Fermat sits in his library, huddled over a copy of Arithmetica written by the Greek mathematician Diaphantus in the third century A. D. Turning the page, Fermat comes across the Pythagorean equation: x 2 + y 2 = z 2. He leans back in his chair to think and wonders if this property is limited to the power of two only. He bends over the book again, scanning ahead through the pages to look for any clues. Suddenly, he begins writing intensely in the margin: â€Å"It is impossible for a cube to be written as a sum of two cubes, or for a fourth power to be written as the sum of two fourth powers or, in general, for any number which is a power greater than the second to be written as a sum of two like powers. I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.† These words, written so carelessly, were to survive to bewilder, frustrate and elude mathematicians of all kinds for centuries to come. This is the legend of Fermat’s Last Theorem. Pierre de Fermat was born in the town of Beaumont-de-Lomagne in southwestern France at the beginning of the seventeenth century in the year 1601. Being the son of a wealthy merchant, Fermat was able to gain a privileged education at monasteries and universities. The young man, however, never showed any particular strength in the subject of mathematics, choosing instead to pursue a career in the civil service of France. His elevated status in society allowed him to include the â€Å"de† in his surname. He suffered a serious attack of the plague during his adult life, severe enough to prompt friends to mistakenly pronounce him dead! Fermat never made math his career, but mathematics at th... ... Kolata, Gina. â€Å"How a gap in the Fermat proof was found.† The New York Times, 144 (January 1995): B5. Expanded Academic ASAP. Middlebury College, Middlebury, VT. 15 September 2002. Mackenzie, Dana. â€Å"Fermat’s Last Theorem Extended.† Science 285.5425 (July 1999): 178. Expanded Academic ASAP. Middlebury College, Middlebury, VT. 15 September 2002. Mozzochi, C. J. The Fermat Diary. American Mathematical Society, 2000. Ribenboim, Paulo. Fermat’s Last Theorem for Amateurs. New York: Springer, 1999. Singh, Simon. â€Å"Fermat’s Enigma: the Epic Quest to Solve the World’s Greatest Mathematical Problem.† New York: Walker, 1997. Van der Poorten, Alf. Notes on Fermat’s last theorem. New York: J. Wiley, 1996. Weisstein, Eric W. â€Å"Fermat, Pierre de.† Wolfram Research. http://scienceworld.wolfram.com/biography/Fermat.html (14 September 2002.)

TERRORISM AND IMMIGRATION Essay -- essays research papers

Terrorism in the United States   Ã‚  Ã‚  Ã‚  Ã‚  The terrifying event that occurred on September 11, 2001 is an example of what the world had been warned about many times, â€Å"TERRORISM†. In 1998, for example, the U.S. government told American citizens that they were potential targets for a terrorist group joined by the now infamous Osama bin Laden (Eland, 1998). However, many did not think any terrorist would be capable of the tragedy that leveled the World Trade Center and took many thousands of human lives. Americans thought they could not be touched, especially on their own turf.   Ã‚  Ã‚  Ã‚  Ã‚  While it may be that organizations involved with Bin Laden that are in the United States, and have been for years, there are other groups that U.S. citizens may not be aware of. Many have probably forgotten The Order of the Rising Sun. Members of this group, in 1972, possessed thirty to forty kilograms of bacteria that they planned to put into the American water supply (Yonah, 1999). The nation is a main target for both national and international terrorists. There are numerous foreign groups and governments that target U.S. For example, Libya, Iraq and Iran in addition to groups from Germany and Palestine(Yonah, 1999). While most of the damage done by such organizations has been overseas, their presence is felt in the United States. Almost all foreign terrorist organizations have caused a problem in the United States, in which the primary threats come from Middle East terrorist organizations (Emerson, 2000). The concept that the Middle East groups are more dangerous to the U.S., is not thought of as a prejudice comment. It is a concept that has been realized by both the FBI and CIA(Emerson,2000). The Middle Eastern and Islamic terrorist groups that have members in the United States include the Algerian Armed Islamic Group, Hamas, Hezbollah, the Palestinian group, the Egyptian group, Al Gamat Al Islamiya, the PKK, the Islamic party, and Al- Qaeda, which belongs to Osama bin Laden (Emerson,2000).   Ã‚  Ã‚  Ã‚  Ã‚  Al-Qaeda is the most dangerous in respect to U.S. interests. The group was formed by Osama bin Laden during the 1980s. In 1989, the organization stated it was their duty, and the duty of all Muslims, to kill U.S. citizens and all U.S. allies (2001). Like other groups, some of their plans were stopped such as the 199... ...ble to freely move about the United States, whether they entered legally or illegally, supporting activities such as bombings, assassinations and other methods of destruction aimed at the Western world. The future likely holds a less trustworthy planet and one would guess that questionable people with questionable passports would be denied entry when they get to U.S. borders throughout the twenty-first century. Still, the fact that terrorists have been able to live in the United States unencumbered during the past decade or so is rather chilling. References Alexander, Y. (1999). Terrorism in the Twenty-First Century: Threats and Responses. The World & I, 14, 80. Eland, I. (1998, September 25). The U.S. Government Is Endangering American Citizens. The Cato Institute. [Online]. Available: http://www.cato.org/dailys/9-25-98.html Emerson, S. (2000). INTERNATIONAL TERRORISM AND IMMIGRATION POLICY:STEVEN EMERSON. Congressional Testimony, PG (Reprinted in http://www.elibrary.com. Original publisher not listed). Terrorist Group Profiles. (2000). Dudley Knox Library: Naval Postgraduate School. [Online]. Available: http://web.nps.navy.mil/~library/tgp/tgp2.htm

conscription Essay example -- essays research papers fc

Non-essential Conscription   Ã‚  Ã‚  Ã‚  Ã‚  As the war on terrorism continues more troops in Iraq and Afghanistan are dying every month. The government is struggling to organize the number of soldiers maintaining the opposition in both Afghanistan and Iraq which brings up a popular topic-conscription (mandatory military enlistment). Senator Charles Rangel of New York was the one that introduced the call for the military draft upon the Senate. The draft was revoked and still hasn’t been in affect since the Vietnam War over thirty years ago. Reinstitution of conscription would not help this country right now, it will just make matters worse. It is not necessary to permit a draft in the United States because our advanced voluntary military should be able to control the defense of our country.   Ã‚  Ã‚  Ã‚  Ã‚  If years from now we are still fighting in operation Iraqi freedom and record numbers of troops are dropping, then congress should start to propose a draft, not now. They probably are pre-warning us right now yet won’t actually pass this mandate until next year or months from today. Who knows, the government can construct a draft tomorrow if they feel that it’s necessary.   Ã‚  Ã‚  Ã‚  Ã‚  A meeting between democrats and republicans took place in January this year regarding conscription. They basically discussed how and when this will take action. â€Å"The middle class and lower middle class should not be forced to bear the burden of fighting and dying if, in fact, this is a generational war.† (Senator Chuck Hagel-Republican from Nebraska) He and many other senators made it clear to the press that if there was a draft, then the majority of the upper middle class and upper class would be targeted to fight for our country. I agree simply because during the Vietnam War, many children of the higher social layers of society found any possible way to avoid the draft.   Ã‚  Ã‚  Ã‚  Ã‚  Our military defense has the most advanced weapons and protection system in the world. Ever since Bush took place in office, our taxes were contributing towards the expenses of the military. After watching the Department of Defense spend billions of dollars on military needs these last past four years, I wonder why they have to bring up this non-essential topic. This budget that Clinton actually proposed was $277.5 billion for the Sec... ...r paying rent and was in the best shape of my life. It wasn’t that bad, also when I was deployed to Iraq I saved a lot of money and came back to the States feeling and living great. The reason why I got out is because I wanted to go to school.   Ã‚  Ã‚  Ã‚  Ã‚  Every person in the U.S. between the ages of 18-26 should be aware of this situation that can possibly happen. They should all have the right to be heard and share their opinions with the rest of the country instead of just the Pentagon, Senate, Legislatures and Politicians. They aren’t the ones who are going to be forced to fight, we are, and we as the young people of society are the easiest intentions. From my knowledge and what I’ve seen while I was in the Army I can say that our armed forces are fine over in Iraq. We don’t need to draft more troops for the war in Iraq. While conscription will ruin our country, another country will be benefited doesn’t make sense. Works Cited http://grassley.senate.gov/won/2003/won02-01-10.htm http://www.defenselink.mil/news/Feb2000/b02072000_bt045-00.html http://www.wsws.org/articles/2004/apr2004/draf-a22.shtml   Ã‚  Ã‚  Ã‚  Ã‚     Ã‚  Ã‚  Ã‚  Ã‚  

Questions in a Little Dark Corner

â€Å"Who are you? Is this me? Why can't I recognize myself?† those questions have always been around me in the pass few years that I have hided myself in a little dark corner. I have asked the same questions to myself over and over again, but when can I get an answer? I've only got more and more questions come out through my mind. I don't know where they came from, I don't what to say, and I don't know what to do, but cry, in a little dark corner. I started to ask those questions when I came to America. I don't know why, but I do know this have never happened to me before. Back in Taiwan, I was known as a cute little girl that likes to play a lot, many adult loves me by make them happy. I know I have come from a beautiful little island, which we all called Taiwan. I never thought about going anywhere outside of this country, until my father has already decided to start a new adventure at America. He thinks this is a good opportunity for us to see outside of the world, and learn something new form the out side world. But are you sure this is a right thing to do? Nobody knows, not even myself. Socratic Seminar Questions I have no idea what's like to be apart from my country, I just know I'm following my dad's order, and go on to the airplane just as he tell me to. I only know few words in English, like â€Å"hello† and â€Å"good bye†, or the most important one â€Å"bathroom†. I still remember when we came down from the airplane, we were lost in the airport, since my older sister have the best English out of all of us, my father tried to convince her to ask direction for us, but still she is also have never talk to any American before, therefore we are all dislike to talk to anyone. But we still need direction for our way out, and then we have the idea to use paper-rock-scissor to decide who will be the one asking direction for us. This â€Å"paper-rock-scissor† thing has happen through out the whole first year that we came to America. Even we have already been practiced talking to native speakers, I don't know why I still didn't see any improvement of my English skill, and I'm the only one still on the same spot as I came to America. I have never liked to talk to any American; I know if I don't talk my English skill will never get better, but what can I do? I can't, just can't, I'm afraid to make any mistakes or see other people make joke out of me, I don't want to make fun of myself and let people laugh at my face. I don't know what to do, what can I do? At the school, because of my â€Å"afraid†, I didn't talk to any other students; therefore I didn't have any friend. Everyone think I'm weird, no one likes to talk to me, and there are even have some classmate thought I'm one of the â€Å"special kid†; they don't like me, and I don't like them, I'm all alone. But is this what I really want? No, I do not want my life continue like this. I want to make some friends, be part of them, have some laugh with, and be happy. Don't walk away from me, don't turn your face away, look at me and talk to me, be friend with me, but how? I keep asking myself to speak, to talk, just open my mouth, but why can't I do it? Why? I ask myself in a dark corner. After one year, when I know we are moving, and I was going to transfer to another school, I was so happy; I thought I can make up my stupid mistake, and make some friends this time. By the time before the first day to my new school, I was teaching myself how to introduce myself to other classmates in front of my bathroom mirror, think that I can actually make some friend on my own. I was very happy; I thought I don't need my little corner any more. But I was wrong. I didn't make up any of my mistakes, I have done it again. When I saw other students came to me, my mouth immediately closed up, and I only stand there and watch them walk pass through me one by one. I hate myself, hate that couldn't speak, hate why can't I just do it, and make some friends. I'm back in the little dark corner, I said to myself everyday, to talk, to speak, to make friend, but I never did it, I can't, not even I wanted to, my mouth just won't work. What can I do? I keep asking myself the same question again and again. Two years have passed my sister and my brother has getting better and butter in English, and they have make all kinds of friends, only I haven't change much, and still no friend for me. High school is getting closer and closer, only few mouth left, I know what I need to do, I know what I should do, but can I do it? I keep practicing my little speech to myself, will I make friends? Will I open my mouth? I don't know, but I will try. I will try anything to get out of the little dark corner. Now I'm a high school student, the little dark corner is getting smaller and smaller; I have friends now, and I even have by â€Å"BFF†, and I'll continue to make more friends. I do not need my corner anymore. But still, I will like to become more open like what I use to be, the happy little girl who always have a nice smile on the face, and make everyone laugh all the time. Even I'm not a little girl anymore, to be happy or sad, I'm still me, I may change over time, but I am still here. This is the new me, to get stronger and stronger, to help other get out of the little dark corner.

Corporal Punishment Argument Essay

Corporal Punishment Argument Essay Corporal Punishment should not be enforced to teach children from misbehaving. To spank and to hit children in todays society Is considered morally wrong but often unpracticed. There is a fine line between abusive hitting and spanking your child on the caboose. Parents who hit their children wither at home or in public leave mental and physical scars that could untimely influence violent behavior in children. Children who are physically punished at home hardly ever learn their lesson.Researchers from the Catalog of Physiologic Study have proved that punishing a child through corporal punishment only leads to more misbehaver. Instead, by confronting them in a calm matter has shown to work better by 35 percent, rather than hitting. In addition, by taking away something that the child possess dear to their hearts for a certain period of time forces them to behave in an orderly manner. For example, when a child runs up a cell phone bill, it would make m ore sense to take away the cell phone rather than physically spank the child and allowing them to keep the cell phone.By keeping the cell phone, children are more likely to take risks. Although, by taking away the phone children understand if they were to take another risk they would jeopardize not having a phone. Society can be viewed as extremely hypocritical. Their viewpoints on public corporal punishment can be seen as evil. More than 90 percent of the community disagrees with corporal punishment while they are in public, but only 15 percent will practice what they preach in their homes. This leaves about 85 percent of parents who exercise spanking in the comfort of their own homes.This hypocritical trait is what leads to frustration in parents and confusion in children. Many times the frustration from not being able to punish children in public leads to a more severe punishment at home. This is often seen when teachers notify higher authority when they see or suspect some sort of violence in their student’s homes. A child who receives corporal punishment undergoes more stress and emotional discomfort than any parent might from contributing punishment. The children’s helplessness can lead to more violent behavior; In addition, most children grow up to mimic the methods of discipline from their own parents or guardians.In 2008, child services survey announced that children who had been spanked at a younger age were at high risk of emotional damage, which often resulted to a poor and unsuccessful future. In addition most children loose respect and become accustomed to being hit by their parents. Most children aren’t fazed by others emotions because of their adapted ways. Spanking and hitting children are not the only idealistic methods to solving problems. The many viewpoints from parents, society and children are important to follow inorder to have a child who

Discuss Dickens treatment of the Victorian concept Essay

Discuss Dickens treatment of the Victorian concept of a gentleman in â€Å"Great Expectations†. Great Expectations is a novel about a boy called Pip and is of him growing up. One day a lawyer turns up at his sister’s house saying he has great expectations of him. A mysterious benefactor is giving money through the lawyer to Pip. Pip spends this money on what he thinks is becoming gentleman i. e. buying new furniture. However towards the end of the novel, when Pip finds out who his mysterious benefactor really is, he realises what a true gentleman is, a man of great principles and, a person with good manners. The novel is written by a much older Pip looking back at his life and being amazed at some of the mistakes he actually made. In Great Expectations, every character has there own opinion of what a real gentleman should be like. Pip, the main character of the novel; while he is still a teenager thinks that a real gentleman should have a lot of money, wear expensive clothes, know how to read and write and should go to a gentleman’s club. Whereas towards the end of the novel, when he is much more grown up, he realises that a true gentleman has good manners and is loyal. Dickens wrote this novel in many sections, which appeared in a newspaper, as the story became so famous the sections were collaborated into a novel. The novel was written in Victorian times, and like many of his novels they were about the times and the attitudes of all people of society. In this novel Dickens’s message to the Victorian people was that to be true gentleman one did not have to be of a rich family or have lots of money; but a true gentleman was loyal, treated others with great respect and had immaculate manners. In modern society we all think that a gentleman should treat others with respect, dress smartly, have excellent manners and be well behaved in public. However some people follow the literal meaning of a gentleman, being that the individual comes from a noble / family. In the novel Pip makes friends with Bently Drummel, who is a gentleman by definition of a dictionary, however what Pip realises a true gentleman is, Bently Drummel is not. There are many things about Bently Drummel that convinces the reader that Bently Drummel is not a true gentleman. Firstly for example he beats his wife, which a true gentleman would never do. A true gentleman would treat a lady with respect at all times. Bently Drummel is only a gentleman because he comes from a rich family his ethics are all completely wrong. He does not lens any money to his friends and he treats them as if they are inferior to him due to his riches. We all know that a true gentleman would never mistreat his friends and would always take great care f them. However on could also argue against these accusations, which are against Bently Drummel and say that he is in fact quite a gentleman. But that all depends upon what one defines a gentleman as. If one says that a gentleman is someone who is very arrogant, and loves himself and his riches more than anyone else then you could say that Bently Drummel is a gentleman However I think in modern day society, and what dickens is trying to put across to the reader is that it is not ones position in society; it is not ones riches that make him a gentleman but his humility, his kindness and his love for his neighbours. In the Victorians times, in which the paper is set, the book as we have said was published in small sections in the newspaper and middle and even lower class people would get to read these newspaper one way or another, so Dickens’s message is not just to the rich or just to the poor but to the whole society. Another example of gentleman by definition and a true gentleman is of Compeyson and Magwitch Magwitch is not rich nor of noble decent, but has good principles, he is Pips mysterious benefactor who sends him money in order for him to become a gentleman, although it may not seem so due to the events early in the novel but Magwitch is kind and caring, as he makes sure that Pip is well looked after. Having said that Magwitch is an escaped convict yet he earns money via an honest living from which he sends money to Pip. Compeyson was Magwitch’s accomplice who ran away with all the money and blamed all the crimes on Magwitch who served the time. Another thing against the Compeyson is that he had very bad principles compared to Magwitch. He conned Miss Havisham into loving him and then and on their wedding day he left Miss Havisham waiting at the altar and ran away with most of her money. This left Miss Havisham devastated she sat I a room with all the clocks stopped at the time of the wedding, she sat their in her wedding gown, very frail obviously because she was not eating well. A true gentleman could never do this to a women and this is highlighted in the way that Magwitch treats women. At the time in which this novel was released in its different sections, Dickens wanted to add enough suspense so that the reader wanted to read the next section and would remember all the previous sections. He added thrill and excitement to the section by introducing a new character relatively in each section, who has there own appearance, is from there own part of society i. e. working class, and who has their own different views and opinions. This is clearly apparent as each character has his own view, for example Estella a beautiful girl, who Pip is deeply in love with tells him that a gentleman dresses smart, has nice shoes and soft hands. IT is clear to see the message that dickens is broadcasting to the people through his novel and is seem to have an effect because it tells all the people the rich and poor that money does not make a gentleman in the eyes of the community so it is better to be happy with what one has and to have good principles and scruples.

Benguet Corporation Essay

1. Statement of the problem The Benguet Corporation refused to submit concentrate samples to the Philippine Associated Smelters and Refining Corporation (PASAR). The Benguet Corporation faces shortage in producing their products and complying its contract to Mitsubishi Metal Corporation and complying the LOI. 2. Analysis of the case  Strengths The Benguet Corporation is the major producer of copper concentrates. It was the oldest mining company, the largest gold and chromite producer and one of the largest copper producers in the Philippines. Smelted Weaknesses Benguet Corporation production was expected to decline steadily which results a negative impact to Mitsubishi Metal Corporation. The Letter of Instruction (LOI) ensures the Philippine Associated Smelting and Refining Corporation (PASAR) an adequate supply of copper concentrates from all local companies which results/causes pressure to Benguet Corporation in submitting its samples to PASAR. Opportunities-chance,break It is the biggest and oldest mining corporation started since 1903 and produces largest gold, chromite and copper in the Philippines. It is active in exploration for gold, copper, chromite and coal. Its expertise is about exploration, mining, beneficiation and marketing of minerals. Threats Benguet Corp. faces complaint from own shareholders. It also fears from selling their concentrates to foreign smelting and refining plants because  of the mercury content which results Benguet enter into a 12year contract to Mitsubishi Metal Corporation. 3. Alternative Solutions to the problem The Benguet Corporation provides 5-year summary of financial performance, including the individual subsidiaries’ contributions and the resulting effects which results of return of the company stakeholders. The Benguet Corporation tried to have a partnership to different small mining corporations which results higher operation employment and workers. Since, Benguet Corporation worriedly looked for foreign buyers of its concentrates. The corporation decided to have a partnership with other foreign smelting and refining companies that could help them mercury content of their products. The LOI helps the Philippine Industry to lessen its dependence of foreign especially Japanese smelter who processed most of the local mining outputs which PASAR does it best to cater the local mining corporations here in Philippines. Since Benguet Corporation could not possibly meet its contract to Mitsubishi and fulfill its quota to PASAR, the Benguet Corporation must submit first its concentrates to PASAR to refine it before giving it to Mitsubishi Corporation to lessen the refining and smelting charges of the Japanese Corporations, so there will be no reimbursement of the total project price and there will be no contractual and workers would be affected. 4. Pointed Solution The Letter of Instruction (LOI) was executed not for negative purposes but for the good of all mining corporations. These is the reason why the LOI 1387 forced and mandated all the local mining corporations to submit their products to the Philippine Associated Smelting and Refining Corporation (PASAR) for testing, refining and smelting of mining products before transporting it to the foreign companies but the Benguet Corporation president, Mr. Jaime V. Ongpin is doubtful to PASAR’s capability in smelting  and refining their products. The reason why Benguet Corporation-PASAR Controversy. Yes the PASAR encountered difficulties on its first year but everyone deserves second chance. I believe that PASAR could help the Beguet Corporation on its problem about smelting and refining its concentrates and to lessen the mercury on its mining products.